Japanese Patent Provisional Publication No. 6-227280 has proposed a preceding vehicle follow-up control apparatus which controls a vehicle speed V at a target vehicle speed Vt. The target vehicle speed Vt for keeping a vehicle-to-vehicle distance to a preceding vehicle at a target distance is calculated on the basis of the vehicle speed V, a difference .DELTA.R between the detection value of the vehicle-to-vehicle distance and the target distance, a gain Gv which is a function of the vehicle speed V, a gain Gr which is a function of the distance difference .DELTA.R and a gain Gd which is a function of a relative speed .DELTA.V from the following equation. EQU Vt=Gv.multidot.V+Gr.multidot..DELTA.R+Gd.multidot..DELTA.R
However, since this conventional preceding vehicle follow-up control apparatus is basically arranged to construct a control system for converging the vehicle-to-vehicle distance to the target distance, it is possible that a relative speed between the vehicles will become too high or too low during the control of the vehicle-to-vehicle distance to the target vehicular distance although the relative speed becomes 0 by the convergence of the vehicle-to-vehicle distance to the target distance. Further, since the conventional preceding vehicle follow-up apparatus is arranged to calculate the target vehicle speed of a controlled vehicle by using a plurality of gains as shown in the above equation, the following problems will occur.
(1) Since these gains are determined experimentally, the steps for tuning thereof becomes large, and the gains become different according to the liking of staffs and a difference of ability among individuals.
(2) Since each gain is stored in the form of an equation or table, a required storage capacity of a memory is increased and the load for calculation processing of a microcomputer is increased.
(3) Since a nonlinear control system, which employs the gain Gd as to the relative speed .DELTA.V and the vehicular distance .DELTA.R in the form of product therebetween, is applied, it is not certain that this control system can preferably converge all follow-up cruising conditions.